Is it possible to get this glossy shiny texture?
Lightning doesn't work the way in blender as blender is similar to the real world reflections and the logo containing the reflections are not even close to the reflections in blender. I've tried it my self in blender after seeing this question.

You can see it in this .gif file below as I try to increase the roughness reflections change.



If you really want to design logo in blender you can using some complex lightning but it won't be as perfect as you wanted, I've tried to make a simple version of what you wanted and this is the final result that I've got. To get this I've put roughness to 0.5 and Clear coat to 1.0

And this is the simple scene that I've made to get the result.



If you want check out the .blend file



Simple Answer : To get the logo you required try "Adobe Illustrator" that would make things easy and simple for making logo as most of the logo making is done in Illustrator and also the logos that you've sent are also Vectors if I'm not wrong.

But if you just want to make in blender try the above scene.